def veExtensionUpdater(t, y, pdict):
#interior function for incompressible background flow only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
N = pdict['N']
M = pdict['M']
l = y[range(2 * N * M)]
l2col = np.reshape(l, (N * M, 2))
l3D = np.reshape(l, (N, M, 2))
P = np.reshape(y[(2 * N * M):], (N, M, 2, 2))
Ps = np.reshape(P, (N * M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate deformation matrix and its inverse
F = SD2D.vectorGrad(l3D, pdict['gridspc'], N, M)
F = np.reshape(F, (N * M, 2, 2))
Finv = CM.matinv2x2(F)
#calculate new velocities at all points of interest (Lagrangian points and force points)
ub, gradub = pdict['myVelocity'](pdict, l, l2col)
lt = ub + pdict['gridspc']**2 * CM.matmult(pdict['eps'], pdict['mu'],
l2col, l2col, Pd)
#calculate new stress time derivatives
gradlt = pdict['gridspc']**2 * CM.derivop(pdict['eps'], pdict['mu'], l2col,
l2col, Pd, F)
Pt = np.zeros((N * M, 2, 2))
for j in range(N * M):
Pt[j, :, :] = np.dot(gradub[j, :, :], Ps[j, :, :]) + np.dot(
np.dot(gradlt[j, :, :], Finv[j, :, :]), Ps[j, :, :]) - (
1. / pdict['Wi']) * (Ps[j, :, :] - Finv[j, :, :].transpose())
return np.append(lt, Pt.flatten())
def viscoElasticUpdaterKernelDeriv(t, y, pdict):
#interior function for force pts only
#split up long vector into individual sections (force pts, Lagrangian pts, stress components)
if 'forcedict' not in pdict.keys():
pdict['forcedict'] = {}
pdict['forcedict']['t'] = t
N = pdict['N']
M = pdict['M']
Q = len(y) / 2 - N * M - 2 * N * M
fpts = np.reshape(y[:2 * Q], (Q, 2))
l = y[range(2 * Q, 2 * Q + 2 * N * M)]
l2col = np.reshape(l, (N * M, 2))
l3D = np.reshape(l, (N, M, 2))
allpts = y[:2 * Q + 2 * N * M] #both force points and Lagrangian points
ap = np.reshape(allpts, (Q + N * M, 2))
P = np.reshape(y[(2 * Q + 2 * N * M):], (N, M, 2, 2))
Ps = np.reshape(P, (N * M, 2, 2))
#calculate tensor derivative
Pd = pdict['beta'] * SD2D.tensorDiv(P, pdict['gridspc'], N, M)
Pd = np.reshape(Pd, (N * M, 2))
#calculate spring forces
f = pdict['myForces'](fpts, pdict['xr'], pdict['K'], **pdict['forcedict'])
#calculate deformation matrix and its inverse
gl = SD2D.vectorGrad(l3D, pdict['gridspc'], N, M)
gls = np.reshape(gl, (N * M, 2, 2))
igls = CM.matinv2x2(gls)
#calculate new velocities at all points of interest (Lagrangian points and force points)
lt = pdict['gridspc']**2 * CM.matmult(
pdict['eps'], pdict['mu'], ap, l2col, Pd) + CM.matmult(
pdict['eps'], pdict['mu'], ap, fpts, f)
#calculate new stress time derivatives
glst = pdict['gridspc']**2 * CM.derivop(
pdict['eps'], pdict['mu'], l2col, l2col, Pd, gls) + CM.derivop(
pdict['eps'], pdict['mu'], l2col, fpts, f, gls)
Pt = np.zeros((N * M, 2, 2))
for j in range(N * M):
Pt[j, :, :] = np.dot(np.dot(glst[j, :, :], igls[j, :, :]),
Ps[j, :, :]) - (1. / pdict['Wi']) * (
Ps[j, :, :] - igls[j, :, :].transpose())
return np.append(lt, Pt.flatten())